Related papers: Modular representations of exceptional supergroups

We show that the classification of simple finite group schemes over an algebraically closed field reduces to the classification of abstract simple finite groups and of simple restricted Lie algebras in positive characteristic. Both these…

We characterize finite-dimensional thick representations over ${\Bbb C}$ of connected complex semi-simple Lie groups by irreducible representations which are weight multiplicity-free and whose weight posets are totally ordered sets.…

In this paper we look into the structure of finite-dimensional graded superalgebras of various types such as associative, Lie and Jordan over an algebraically closed field of characteristic zero.

We classify the module categories over the double (possibly twisted) of a finite group.

We classify, up to isomorphism, all gradings by an arbitrary abelian group on simple finitary Lie algebras of linear transformations (special linear, orthogonal and symplectic) on infinite-dimensional vector spaces over an algebraically…

We classify all conformal irreducible modules of finite type over the Cheng Kac superalgebra CK(6).

We prove the existence of certain rationally rigid triples E8 in good characteristic and thereby show that these groups over the prime field occur as Galois groups over the field of rational numbers. We show that these triples give rise to…

Let G be an almost simple, simply connected algebraic group over an algebraically closed field of characteristic p>0. In this paper we restate our conjecture from 1979 on the characters of irreducible modular representations of G so that it…

Let G be a finite group and let p be a prime. A module for G over a field of characteristic p is called algebraic if it satisfies a polynomial, with addition and multiplication given by direct sum and tensor product. In some sense, having…

Let $G$ be a finite group and let $F$ be a finite field of characteristic $2$. We introduce \emph{$F$-special subgroups} and \emph{$F$-special elements} of $G$. In the case where $F$ contains a $p$th primitive root of unity for each odd…

In this paper, we first present a classification theorem of infinite-dimensional simple Novikov algebras over an algebraically closed field with characteristic 0. Then we classify all the irreducible modules of a certain…

We construct a new family of irreducible modules over any basic classical affine Kac-Moody Lie superalgebra which are induced from modules over the Heisenberg subalgebra. We also obtain irreducible deformations of these modules for the…

We classify all linearly compact simple Jordan superalgebras over an algebraically closed field of characteristic zero. As a corollary, we deduce the classification of all linearly compact unital simple generalized Poisson superalgebras.

Let G be a simple algebraic group over an algebraically closed field k. We classify the spherical conjugacy classes of G.

Let A be a finitely generated associative algebra over an algebraically closed field. We characterize the finite dimensional modules over A whose orbit closures are regular varieties.

Over algebraically closed fields of characteristic p>2, prolongations of the simple finite dimensional Lie algebras and Lie superalgebras with Cartan matrix are studied for certain simplest gradings of these algebras. Several new simple Lie…

Let G be a connected and reductive algebraic group over an algebraically closed field of characteristic p > 0. An interesting class of representations of G consists of those G-modules having a good filtration -- i.e. a filtration whose…

For a type I basic classical Lie superalgebra $\mathfrak{g}=\mathfrak{g}_{\bar{0}} \oplus \mathfrak{g}_{\bar{1}}$, we establish an equivalence between typical blocks of categories of $U_{\chi}(\mathfrak{g})$-modules and…

Primarily this paper presents an expository report on alternatives to the traditional methods of classifying representations of finite dimensional algebras. Some new results illustrating such alternatives for algebras with only finitely…

We identify an interesting special class of prime ideals in the finitary infinite symmetric group algebra. We show that the set of such ideals carries a semiring structure. Over the complex numbers, we establish a connection with spherical…